周期伪轨跟踪性与伪轨跟踪性的关系

Relationship between the periodic pseudo-orbit-tracing property and the pseudo-orbit-tracing property.

设(X,d)为紧致度量空间,f是X上的连续自映射.首先证明了:若f具有周期伪轨跟踪性,则f的链回归集与周期点集的闭包相等,即CR(f)=P(f).然后利用此性质,给出了一个具有伪轨跟踪性但不具有周期伪轨跟踪性的例子.最后给出了伪轨跟踪性蕴含周期伪轨跟踪性的两个充分条件.

Let（X,d） be a compact metric space,and f：X→X be a continuous map.It is proved that if f has the periodic pseudo-orbit-tracing property,then its chain recurrent set of f will be equal to the closure of the periodic point set（i.e.CR（f）=P（f））.An example is given for a map which has the pseudo-orbit-tracing property,but doesn＇t have the periodic pseudo-orbit-tracing property.In addition,two sufficient conditions are proved for the pseudo-orbit-tracing property to be the periodic pseudo-orbit-tracing properly.